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Breadth first search. Breadth first search. Structures for BFS. Implementation. ( Δ , D) – graph. Breadth first search. BFS by practice. We start from a source node. We want to see if we can reach a target node. We proceed by waves. target. source. Breadth first search. - PowerPoint PPT Presentation
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Breadth first search
Breadth first search
Breadth first search
Structures for BFS
Implementation
(Δ, D) – graph
BFS by practiceBFS by practice
target
Breadth first search
We start from a source node. We want to see if we can reach a target node. We proceed by waves.
source
target
Breadth first search
We start from a source node. We want to see if we can reach a target node. We proceed by waves.
source
3 waves total.
target
Breadth first search
source
• a Queue, in which we add neighbours and from which we select the next one to visit
• a Dictionary: to each node that we visited we bind as value its predecessor.
2 data structures
pred: Robin
pred:
Pranil
pred:
Pranilpred:
Pranil
pred:
Shivam
pred:
Danishpred:
Awin
ImplementationImplementation
((ΔΔ, D) – graph , D) – graph
Distance
Breadth first search
The number of hops it takes to go from A to B is called the distance from A to B and denoted d(A,B).
1 hop
2 hops
3 hops
d(Pranil,Som) = 3
Distance
Breadth first search
The number of hops it takes to go from A to B is called the distance from A to B and denoted d(A,B).
2
d(Danish,Aram) = 2
1
We use the shortest path.
Diameter
Breadth first search
The diameter of a graph is the maximum distance between two vertices, and is denoted D.
D = 5
(Δ, D) – graph
Breadth first search
Let Δ be the maximum degree in a graph, i.e. the largest number of neighbours that any node can have. Let D be the diameter.
For a given Δ and D, design the graph having as many nodes as possible.
Example: we want to create a good network of workstations. Each workstation can be connected to at most 3, and the diameter must be 1.
The best (3, 1) – graph has 4 nodes.
(Δ, D) – graph
Breadth first search
Let Δ be the maximum degree in a graph, i.e. the largest number of neighbours that any node can have. Let D be the diameter.
For a given Δ and D, design the graph having as many nodes as possible.
The best (3, 1) – graph has 4 nodes.
Practice: draw the best (3, 2) – graph possible.
(Δ, D) – graph
Breadth first search
Practice: draw the best (3, 2) – graph possible.
5 6 7
8 10
Breadth first search
Breadth first search
Pavol Hell, SFU
Jean-Claude Bermond, Université de Nice
The network teams from Nice and SFU are associated.
